This hurts my head to ask, but - is there a way to alter the path of backup jobs?

Since your OS is compatible, it should just work if you change your paths in the configuration.

It will be slow for the first backup, because it needs to read all files again and probably the metadata is changed, so it might need to upload that. But the content is already in the backup, so it will not be stored again.

On the restore side you will just have a break where the old versions have old paths and any new versions have the new paths, but the common path prefix is stripped anyways if you select a target folder.